The IIe has a built-in self test. One website suggests that you access it by pressing control, solid-apple, reset (though I thought it was solid-apple, hollow-apple, reset). I'm not sure how indepth it is, but it may help you find the problem.

Quite frankly though, the Apple gear sounds boring. (And yes, this is from an Apple II enthusiast.) The Mac gear though sounds intensely interesting since pre-System 6 and pre-Mac Plus era stuff seems to be scarce these days. What sort of stuff did you get on those MFS floppies?